accurate {aTSA}  R Documentation 
Computes the accurate criterion of smoothed (fitted) values.
accurate(x, x.hat, k, output = TRUE)
x 
a numeric vector of original values. 
x.hat 
a numeric vector of smoothed (fitted) values. 
k 
the number of parameters in obtaining the smoothed (fitted) values. 
output 
a logical value indicating to print the results in R console. The default is

See http://www.dms.umontreal.ca/~duchesne/chap12.pdf in page 616  617 for the details of calculations for each criterion.
A vector containing the following components:
SST 
the total sum of squares. 
SSE 
the sum of the squared residuals. 
MSE 
the mean squared error. 
RMSE 
the root mean square error. 
MAPE 
the mean absolute percent error. 
MPE 
the mean percent error. 
MAE 
the mean absolute error. 
ME 
the mean error. 
R.squared 
R^2 = 1  SSE/SST. 
R.adj.squared 
the adjusted R^2. 
RW.R.squared 
the random walk R^2. 
AIC 
the Akaike's information criterion. 
SBC 
the Schwarz's Bayesian criterion. 
APC 
the Amemiya's prediction criterion 
If the model fits the series badly, the model error sum of squares SSE
may be larger than SST
and the R.squared
or RW.R.squared
statistics
will be negative. The RW.R.squared
uses the random walk model for the purpose of
comparison.
Debin Qiu
X < matrix(rnorm(200),100,2)
y < 0.1*X[,1] + 2*X[,2] + rnorm(100)
y.hat < fitted(lm(y ~ X))
accurate(y,y.hat,2)